Further Mathematics Past QuestionsQuestion 26:If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} + 5x + n = 0\), such that \(\alpha\beta = 2\), find the value of n. A. -4 B. -2 C. 2 D. 4 Question 27:Solve \(\log_{2}(12x - 10) = 1 + \log_{2}(4x + 3)\). A. 4.75 B. 4.00 C. 1.75 D. 1.00 Question 28:Find the coefficient of \(x^{3}\) in the binomial expansion of \((x - \frac{3}{x^{2}})^{9}\). A. 324 B. 252 C. -252 D. -324 Question 29:The general term of an infinite sequence 9, 4, -1, -6,... is \(u_{r} = ar + b\). Find the values of a and b. A. A = 5, b = 14 B. A = -5, b = 14 C. A = 5, b = -14 D. A = -5, b = -14 Question 30:If \(\begin{vmatrix} k & k \\ 4 & k \end{vmatrix} + \begin{vmatrix} 2 & 3 \\ -1 & k \end{vmatrix} = 6\), find the value of the constant k, where k > 0. A. 1 B. 2 C. 3 D. 4 |
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